# What is the period of f(t)=sin( t / 36 )+ cos( (t)/16 ) ?

Mar 15, 2017

$288 \pi$

#### Explanation:

Period of $\sin \left(\frac{t}{36}\right)$ --> $36 \left(2 \pi\right) = 72 \pi$
Period of $\cos \left(\frac{t}{16}\right)$ --> $16 \left(2 \pi\right) = 32 \pi$
Find least common multiple of 32 and 72.
$32 - \to {2}^{3} \cdot 4 - \to 32 \cdot 9 = 288$
$72 - \to {2}^{3} \cdot 9 - \to 72 \cdot 4 = 288$
Period of f(t) --> $288 \pi$